A073919 Smallest prime p with bigomega(p-1)=n, where bigomega(m)=A001222(m) is the number of prime divisors of m (counted with multiplicity).

2, 3, 5, 13, 17, 73, 97, 193, 257, 769, 3457, 7681, 15361, 12289, 40961, 114689, 65537, 737281, 1376257, 786433, 5308417, 7340033, 14155777, 28311553, 104857601, 113246209, 167772161, 469762049, 2113929217, 1811939329

Offset

0,1

Links

David W. Wilson and Robert G. Wilson v, Table of n, a(n) for n = 0..351

Example

a(2) = 5 = 2*2 + 1. a(5) = 73 = 2*2*2*3*3 + 1.

Mathematica

ptns[n_, 0] := If[n==0, {{}}, {}]; ptns[n_, k_] := Module[{r}, If[n<k, Return[{}]]; ptns[n, k]=1+Union@@Table[PadRight[ #, k]&/@ptns[n-k, r], {r, 0, k}]]; a[n_] := Module[{i, l, v}, v=Infinity; For[i=n, True, i++, l=(Times@@Prime/@#&)/@ptns[i, n]; If[Min@@l>v, Return[v]]; minp=Min@@Select[l+1, ProvablePrimeQ]; If[minp<v, v=minp]]] (* First do <<NumberTheory`PrimeQ`. ptns[n, k] is list of partitions of n into exactly k parts *) Array[a, 30, 0]
With[{x=Table[{Prime[n], PrimeOmega[Prime[n]-1]}, {n, 104000000}]}, Transpose[ Table[ SelectFirst[x, #[[2]]==i&], {i, 0, 29}]][[1]]] (* Harvey P. Dale, Sep 28 2014 *)

Crossrefs

Cf. A118883.

Sequence in context: A355518 A108562 A087523 * A162573 A349785 A087356

Adjacent sequences: A073916 A073917 A073918 * A073920 A073921 A073922

Keyword

nonn

Author

Amarnath Murthy, Aug 18 2002

Extensions

Edited by Dean Hickerson, Nov 12 2002

Status

approved